A confidence interval that is consistent with and more informative than an equivalent test for a normal mean
A confidence interval that is consistent with and more informative than an equivalent test for a normal mean
This note shows how to construct a 1 - ß level symmetric confidence interval for a normal mean ? that is consistent with and more informative than a size ß sequential equivalence test of H0 :|?| > d against the alternative Ha :|? | = d, where d>0 is a prespecified limit of equivalence. If the null hypothesis H0 is rejected and so equivalence can be declared by the test, then the confidence interval is contained in the interval [- d, d]. If the null hypothesis H0 is not rejected and so equivalence cannot be declared by the test, then the confidence interval contains the interval [- d, d]. Therefore the test and the confidence interval are consistent in rejection or non-rejection of H0. But the confidence interval provides extra information on the magnitude of ?, and is therefore more informative than the test.
151-157
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
2003
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Liu, Wei
(2003)
A confidence interval that is consistent with and more informative than an equivalent test for a normal mean.
Sequential Analysis, 22 (1-2), .
(doi:10.1081/SQA-120022088).
Abstract
This note shows how to construct a 1 - ß level symmetric confidence interval for a normal mean ? that is consistent with and more informative than a size ß sequential equivalence test of H0 :|?| > d against the alternative Ha :|? | = d, where d>0 is a prespecified limit of equivalence. If the null hypothesis H0 is rejected and so equivalence can be declared by the test, then the confidence interval is contained in the interval [- d, d]. If the null hypothesis H0 is not rejected and so equivalence cannot be declared by the test, then the confidence interval contains the interval [- d, d]. Therefore the test and the confidence interval are consistent in rejection or non-rejection of H0. But the confidence interval provides extra information on the magnitude of ?, and is therefore more informative than the test.
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Published date: 2003
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Statistics
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Local EPrints ID: 30113
URI: http://eprints.soton.ac.uk/id/eprint/30113
ISSN: 0747-4946
PURE UUID: d9445bac-176b-49dd-bdbb-0993c2db2779
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Date deposited: 19 May 2006
Last modified: 16 Mar 2024 02:42
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